development of an inverse design method for axial ...

DEVELOPMENT OF AN INVERSE DESIGN METHOD FOR PROPELLERS WITH APPLICATION ON LEFT VENTRICULAR ASSIST DEVICES

ENTWICKLUNG EINER INVERSEN AUSLEGUNGSMETHODE FÜR PROPELLER UND DERER ANWENDUNG AUF LINKSVENTRIKULÄRE UNTERSTÜTZUNGSPUMPEN

Der Technischen Fakultät der Friedrich-Alexander-Universität Erlangen-Nürnberg zur Erlangung des Doktorgrades Dr.-Ing.

vorgelegt von Mihai Bleiziffer geb. Miclea

aus Hermannstadt Rumänien

Als Dissertation genehmigt von der Technischen Fakultät der Friedrich-Alexander-Universität Erlangen-Nürnberg

Tag der mündlichen Prüfung:

13.07.2017

Vorsitzender des Promotionsorgans:

Gutachter:

Prof. Dr.-Ing. Reinhard Lerch

Prof. Dr.-Ing. habil. Antonio Delgado Prof. Dr.-Ing. Alexandrina Unt˘aroiu

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Copyright Hinweis Die vorliegende Arbeit verwendet die Schriftart Utopia®. Sie ist von Adobe zur Verwendung durch die TEX Users Group (TUG) freigegeben und unterliegt dem Copyright. Der mathematische Zeichensatz wird durch das Paket Fourier-GUTenberg über das Comprehensive TEX Archive Network (CTAN) zur Verfügung gestellt. Copyright 1989, 1991 Adobe Systems Incorporated. All rights reserved. Utopia® Utopia is either a registered trademark or trademark of Adobe Systems Incorporated in the United States and/or other countries. Used under license.

To Helen and Sophie

Acknowledgments

First, I want to express my deepest gratitude to my mentor Prof. Dr.-Ing. habil. Antonio Delgado for guiding me during the past 9 years, finally adding more value to the present thesis by the suggestions he made during the review. It is due to him that I could go deeper in the fantastic world of fluid mechanics and turbomachinery while working at the LSTM in Erlangen. He not only guided me all these years but he gave me a platform on which I could freely create and develop myself. I have to thank him for encouraging and making my visiting research stage at the University of Virginia possible. He helped me overcome weaknesses and transform them into strengths and further improve myself. I want to express my gratitude to Prof. Alexandrina Untaroiu from Virginia Polytechnic Institute for the suggestions she made to the present thesis and for accepting to be a member in the doctoral examination committee. I also want to thank her for inviting me for a research stage at the University of Virginia while I could work on the validation of the ADAP code. I want to thank Prof. Dr.-Ing. Jovan Jovanovic who not only introduced me to the world of turbulence but also advised me every time I had questions. I also want to thank him for accepting to be the chairman of my doctoral committee. The former group leader of the turbomachinery group at LSTM, Prof. Dr.-Ing Philipp Epple I want to thank for inviting me to join his group and for sharing with me his fan and blower design experience. We have worked together at many interesting industrial projects, where I was able to extend my knowledge in aerodynamics. I want to thank Prof. Dr. Ing. Özgür Ertunç for welcoming me in his research group at LSTM and for many advices he gave me over the time. I am also thankful to Prof. Marc Drela from the MIT for his advice on the numerical cascade simulations and for inspiring me with his work. I express my appreciation to Prof. Dr.-Ing. Jens Peter Majschak from the TU-Dresden who opened me the way to the academic world and offered me the first job as a researcher after finishing my studies. I am also grateful for the support given by the leaders of the turbomachinery group, Bettina Grashof and Matthias Semel. I want to thank my former colleagues Dr. Frauke Groß, Judith Forstner, Dr. Ana Zbogar-Rasic, Jens Krauß, Dr. Manuel Münch, David Botello-Payro, Balkan Genc, and Dr. Giovanni Luzi for the good time we had at LSTM. I also want to thank my bachelor and master students, especially Patrick Töpfer and Ulrich Schlegel for their work with me and for performing most of the measurements presented in this thesis. I am thankful to Dipl.-Ing. Klaus Epple from Cardiobridge Gmbh for the good work during the ZIM funded project, and for providing the first version of the MOCK setup as well as the original P 14F pump. I thank him and the company for allowing me to publish pictures and data of the 14F Reitan Catheter Pump. I also want to thank MD PhD. Oyvind Reitan from the Lund University for sharing with me his work and for helping me understand the physiological impact of a blood pump. Measurements on test rigs would not have been possible without the support given by the LSTM workshop. First I want to thank the head of the LSTM workshop Hermann Lienhart. I want to thank Heinz Hedwig and Herbert Kaiser from the mechanical workshop for building my test rigs. I also want to thank Rolf Zech, Franz Kaschak and especially Horst Weber for helping me build the LDA setup and

VII

all electronic devices needed for the measurements. The IT support provided by Sebastian Röhl and Thorsten Bielke is gratefully acknowledged. For the time I have been at LSTM the secretariat was one of its central points, and its importance grew after I left the institute. I want to thank Mrs. Georgia Bouna, Mrs. Isolina Paulus, Mrs. Anke Lutz and especially Mrs. Franziska Jung for the good cooperation, for organizing my work and helping me keep a good contact to the institute. I also want to thank the administration of LSTM especially to Dr. -Ing. Bernhard Mohr, Sonja Hupfer and Claudia Gerstacker. The financial support for my research stage at the University of Virginia was granted by the Graduate School for Advanced Optical Technologies (SAOT) in Erlangen. I want to thank Dr. Dubravka Melling, PD. Dr Andreas Bräuer and Joana Stümpfig Barrinho for their support and for the good time I had during the SAOT academies. The support of the Edmund-Bradatsch-Foundation for printing this thesis is also gratefully acknowledged. I am grateful to my colleagues and friends Charles Comeau, Aleksandar Sekularac and Tim Weiland for the hard work they have done in reviewing the present thesis. I also thank my friend Jaswinder Singh for a first review and for a lot of support in numerical fluid mechanics. My friend Dr. Ionut Georgescu I would like to thank for encouraging me to follow my dream and for offering me his help every time I needed. Without his advice in Matlab a part of this work would not have been possible. I would like to thank Mrs. Renate Krämer, our friend and neighbour in Worms, for the days I could write undisturbed at her home. I would like to thank my parents for encouraging me to learn and keep persevering in my passion and for the financial support during my studies. I want to thank my grandparents Alice (1925-1989) and Gheorghe Istodorescu (1922-2015) for raising me and teaching me to always be curious and seek for answers. My parents-in-law were a huge source of support for which I am grateful. For her continuous support and unselfish love I would like to thank my wife Helen. She encouraged me to pursue my passion and has been patient the many nights and weekends in the past 9 years while I was working at this thesis. Her support has extended after the birth of our daughter Sophie for who she cared also in my place so I was able to complete this work. Köszönöm és szeretlek teljes szívemb˝ol!

VIII

Contents

List of Figures

XI

List of Tables

XV

1 Introduction 1.1 Short overview of LVAD used in the treatment of cardiogenic shock . . . . . . . . . . . . . 1.2 Design and analysis methods for VADs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Outline and objectives of the dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Selected aspects in relevant areas for the design of VADs 2.1 Design consideration for VADs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Human circulatory system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Blood composition and its physical properties . . . . . . . . . . . . . . . . . . 2.1.3 Considerations on blood damage for VADs . . . . . . . . . . . . . . . . . . . . 2.1.4 Design requirements (duty point of a LVAD) . . . . . . . . . . . . . . . . . . . . 2.1.5 Head characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Governing equations for fluid dynamics and aerodynamics . . . . . . . . . . . . . . 2.2.1 Governing equations for fluid dynamics . . . . . . . . . . . . . . . . . . . . . . 2.2.2 RANS turbulence modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Two-dimensional flows for aero- and hydrodynamics applications . . . . . . 2.3 Air- and hydrofoil families: laminar NACA 6-Digit series . . . . . . . . . . . . . . . . 2.4 Propeller design methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Axial momentum theory for propellers . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Blade element theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Design theory using the radial loss model proposed by Betz and Prandtl . . 2.4.4 Design theory using the radial loss model proposed by Goldstein . . . . . . . 2.4.5 Design method correction for moderately loaded propellers . . . . . . . . . . 2.4.6 Design theory using lifting-line and vortex-lattice theories . . . . . . . . . . . 2.5 Design and construction of a closed loop measurement test rig . . . . . . . . . . . . 2.5.1 Test rig set-up and construction . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Methods and materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Data recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.4 Initialization and characteristics of the LDA flow-rate measurement system . 2.6 Design and construction of a MCL . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

3 Presentation and discussion of the results 3.1 Procedure for designing propellers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Development of a propeller design and analysis code . . . . . . . . . . . . . . . . . . . . . 3.2.1 Numerical solution for thin airfoil cascades . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Sensitivity check for the CV L computational model . . . . . . . . . . . . . . . . . . . 3.2.3 Propeller design framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 An iterative method for correcting the lift distribution for propellers with small pitchto-chord ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2 5 5 7 7 7 8 10 11 12 13 14 16 18 19 21 22 26 28 33 34 34 36 36 40 44 48 50 53 53 54 54 58 68 71

IX

Contents

3.2.5 BEM propeller analysis procedure using the Goldstein loss model . . . . . . . 3.3 Design procedure for multiblade open-water propellers . . . . . . . . . . . . . . . . . 3.3.1 Challenges in designing multiblade propellers . . . . . . . . . . . . . . . . . . . 3.3.2 CFD setup and simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Numerical errors of CFD simulations . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Geometry, grid generation and grid study for the problem . . . . . . . . . . . . 3.3.5 Design parameter study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.6 Discussion of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Design procedure for an encased propeller used as a LVAD . . . . . . . . . . . . . . . 3.4.1 Experimental and CFD assessment of the 14F RCP pressure-flow performance 3.4.2 Analysis of the flow mechanism in the RCP . . . . . . . . . . . . . . . . . . . . . 3.4.3 Design and optimization of new VAD propellers . . . . . . . . . . . . . . . . . . 3.4.4 Validation of new designs by test-rig measurements . . . . . . . . . . . . . . . . 3.4.5 Numerical estimations of blood damage . . . . . . . . . . . . . . . . . . . . . . . 3.4.6 Time-dependent CFD simulations of encased propeller VADs . . . . . . . . . .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .

73 74 74 76 76 77 80 84 90 90 97 100 110 112 118

4 Conclusion and Outlook

121

Bibliography

123

A Derivation of the scalar shear stress σ from the Navier Stokes equations

131

B Computation of RBC mass-flow

135

C Propeller helping device

137

X

List of Figures

1.1.1 1.1.2 1.1.3 1.1.4 1.1.5

2.1.1 2.1.2 2.1.3 2.1.4 2.1.5 2.1.6 2.2.1 2.2.2 2.2.3 2.3.1 2.3.2 2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 2.4.6 2.4.7 2.5.1 2.5.2 2.5.3 2.5.4 2.5.5 2.5.6 2.5.7 2.5.8 2.5.9 2.5.10 2.5.11 2.5.12 2.5.13

The Intra-aortic balloon pump (from [115]) . . . . . . . . . . . . . . . . . . . . . . . . . Hemopump®[97] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Impella 2.5 ® von Thoratec® and its placement [102] . . . . . . . . . . . . . . . . . . . 14F Reitan catheter pump (figure courtesy of Cardiobridge Gmbh/Hechingen) . . . . Physiological position of the 14 F RCP in the upper aorta (figure courtesy of Cardiobridge Gmbh/Hechingen) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 3 3 3 4

Human circulatory system [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Rheological properties of blood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Viscosity vs shear rate for different hematocrit levels (adapted from [29]) . . . . . . . . 9 Shear stress factors contributing to the blood damage . . . . . . . . . . . . . . . . . . . 10 Aortic pressure (AoP) distributions for healthy and severe CS - cases . . . . . . . . . . 12 Cordier diagram following Lewis [52]showing the ideal and existing design points set for a LVAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Local time-average of a fluctuating quantity G . . . . . . . . . . . . . . . . . . . . . . . 15 Energy spectrum of turbulence as function of the wave number k with the application range of CFD turbulence models (adapted from Hirsch [38, pp.88]) . . . . . . . . . . . 17 Two-dimensional slice (airfoil) of a blade . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Sketch of a modern airfoil composed of a mean-line (camber-line) and a thickness distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Comparison between theoretical and experimental lift slopes of airfoils [72] . . . . . . 20 Stages of propeller design and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Exaggerated sketch showing the basis for the actuator disk theory . . . . . . . . . . . . 23 C T,C P and η computed from the axial influence factor a . . . . . . . . . . . . . . . . . 25 Sketch showing both axial and angular momentum components for a propeller . . . . 25 Blade element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Forces and velocities acting on a blade element . . . . . . . . . . . . . . . . . . . . . . . 27 Propeller wake with helical vortices and the concept of displacement velocity (v’) . . 28 System characteristics of pump indicating different losses inside the measurement rig 36 CAD sketch of the loop test rig concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 CFD computed pressure distribution downstream the propeller . . . . . . . . . . . . . 39 Bore for pressure measurement according to DIN . . . . . . . . . . . . . . . . . . . . . . 39 Ready test rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Rosemount G151 pressure transducer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Principle of laser Doppler shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Two-beam LDA setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Laser and optical measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Left hand side: Bandpass filter (LSTM-invent-895-102), right hand side: Philips PM3295A oscilloscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 BBC Görtz LSE 01 Doppler signal processor (frequency tracker) . . . . . . . . . . . . . 44 NI 9178 USB chassis with 3 NI 9215 BNC input modules . . . . . . . . . . . . . . . . . . 45 Front panel of the measurement program . . . . . . . . . . . . . . . . . . . . . . . . . . 45

XI

List of Figures

2.5.14 2.5.15 2.5.16 2.5.17

Measurement software layout in LabView (adapted from [108]) . . . . . . . . . . . . . Computation of the friction velocity (adapted from [108]) . . . . . . . . . . . . . . . . . Computation of the stationary turbulent velocity profile (adapted from [108]) . . . . Pictures showing the setup for the benchmark measurement from left to right: inflow container (at ~2 m height), flow path in the glass pipe with LDA and throttle . . . . . . 2.5.18 comparison of the proposed turbulent profiles . . . . . . . . . . . . . . . . . . . . . . . 2.5.19 Comparison of the volumetric flow-rate computed by using the three turbulent profiles and the balance measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Analogy between the human circulatory system (LHS[1]) and the Mock (RHS)) . . . . 2.6.2 LabView measurement panel for the mock . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.3 Validation of the MCL by comparing AoP to literature and human measurements . . .

45 47 48

3.1.1 3.2.1

53

3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.2.8

3.2.9 3.2.10 3.2.11 3.2.12 3.2.13 3.2.14 3.2.15 3.2.16 3.2.17 3.2.18 3.2.19 3.2.20 3.2.21 3.2.22

3.2.23 3.2.24 3.2.25 3.2.26 3.3.1 3.3.2 3.3.3 3.3.4

XII

General procedure for designing propellers . . . . . . . . . . . . . . . . . . . . . . . . . Sketch of a cylindrical meridian surface through an axial turbomachine and the resulting cascade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Panel method for thin airfoils (reprinted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Infinite row of vortexes (cascade) (reprinted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaluation of the thin flat plate at AO A = 5° with points placed at 0.1 · c . . . . . . . . . Evaluation of the thin flat plate at AO A = 5° with points placed at 0.01 · c . . . . . . . . Evaluation of the thin flat plate at AO A = 5° with points placed at 0.001 · c . . . . . . . C P distribution around a flat plate computed at variable distance from camber . . . . c l results obtained analytically (red) and by the CVL method (green and blue) for circular arcs with different cambers (reprinted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solution of the flat plate @ AO A = 5° with 50 panels . . . . . . . . . . . . . . . . . . . . Solution of the flat plate @ AO A = 5° with 500 panels . . . . . . . . . . . . . . . . . . . . Evaluation of a thin 5% circular arc cambered foil at AO A = 5° . . . . . . . . . . . . . . Evaluation of a thin 15% circular arc cambered foil at AO A = 5° . . . . . . . . . . . . . Lift ratio k as a function of the solidity σ and stagger angle λ (reprinted from MicleaBleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . . . . . . Figure showing computed streamlines around flat plate cascade with a t /l = 1, at AO A = 5° and λ = 30°, 50°, 70° . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaluation of a NACA mean-line (a = 0.8 ,c l = 0.75) at ideal AO A . . . . . . . . . . . . Evaluation of a NACA mean-line (a = 0.8,c l = 1) at ideal AO A . . . . . . . . . . . . . . . Evaluation of a NACA mean-line cascade (a = 0.8,c l = 0.75), λ = 50°and t /l = 1 . . . . Evaluation of a NACA mean-line cascade (a = 0.8,c l = 1), λ = 50°and t /l = 1 . . . . . . Goldstein factor (G) distribution for propellers with 4 and 6 blades . . . . . . . . . . . Overview of the design program ADAP (V 0.973) . . . . . . . . . . . . . . . . . . . . . . ADAP logo, version and copyright agreements written on the top of every file . . . . . Design framework for propellers with high pitch-to-chord ratio as implemented in ADAP (V 0.973) (reprinted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Convergence of the ADAP propeller design code . . . . . . . . . . . . . . . . . . . . . . Figure 1 and Figure 2 from ADAP showing the stacked airfoils and relevant design data Figure 3 and Figure4 from ADAP showing relevant propeller design data . . . . . . . . Structure of the BEM analysis method . . . . . . . . . . . . . . . . . . . . . . . . . . . . Setup of the studied problem (reprinted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Propeller blade geometry in TurboGrid with figured sections . . . . . . . . . . . . . . . Convergence of solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Details of numerical mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48 49 49 50 51 52

55 55 56 59 59 60 60

61 62 62 63 64 64 65 66 66 67 68 68 70 70

72 73 73 74 75 77 78 79 79

List of Figures

3.3.5

3.3.6 3.3.7 3.3.8 3.3.9 3.3.10 3.3.11

3.3.12

3.3.13 3.3.14 3.3.15 3.3.16 3.3.17 3.3.18 3.3.19 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.4.6 3.4.7 3.4.8 3.4.9 3.4.10 3.4.11 3.4.12 3.4.13 3.4.14 3.4.15 3.4.16 3.4.17 3.4.18 3.4.19

Grid study showing the dependence of K T and KQ at design point V = 0.3[m/s] (J = 0.24) upon the number of grid elements (reprinted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Thickness study results for a 4 bladed propeller (reprinted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 C p distribution of both propellers at J = 0.7 and 0.7 span . . . . . . . . . . . . . . . . . 82 C p distribution of both propellers at J = 0.7 and 0.1 span . . . . . . . . . . . . . . . . . 83 Influence of ε in the design framework upon K T and η at design point V = 0.3[m/s] (J = 0.24) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Results of the present design code are given in red and results of mpvl code [20] are given in blue (reprinted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) 84 Thrust and torque characteristics for propellers with (blue) and without (red) the CVL correction, dashed line results of the BEM method (figure adapted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Efficiency characteristics for propellers with (blue) and without (red) the CVL correction, dashed line results of the BEM method (figure adapted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Radial distribution of thrust and torque for design, propeller and propeller with CVL correction (reprinted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) 86 Radial distribution of efficiency at J = 2.4 (reprinted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 C P distribution of the 0.1, 0.3, 0.5 span sections of both investigated propellers at J = 2.4 87 C P distribution of the 0.7, 0.9 span sections of both investigated propellers at J = 2.4 . 88 Suction side of the blade with contours of static pressure (J = 2.4) (reprinted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . 88 Pressure side of the blade with contours of static pressure (J = 2.4) (reprinted from Miclea-Bleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . 89 Normalized axial velocity in an aft propeller plane (J = 2.4) (reprinted from MicleaBleiziffer et al. [59], with permission from Elsevier) . . . . . . . . . . . . . . . . . . . . . 89 CAD Model of the 14F RCP (courtesy of Cardiobridge GmbH) . . . . . . . . . . . . . . . 90 CAD Model of the reconstructed 14F propeller. Right: stereolitography prototype . . . 91 Measurements of the five 14F RCP configurations . . . . . . . . . . . . . . . . . . . . . . 92 CFX setup used for the 14F RCP simulations (lengths are given in mm) . . . . . . . . . 93 Rotor and stator mesh of the 14F setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Output of the CFX mesh statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Convergence history at duty point (5 l /mi n) . . . . . . . . . . . . . . . . . . . . . . . . . 95 Plot of the y+ on the external walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Plot of the y+ on the blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Validation of the CFD results by experimental measurements of the 14 RCP running in water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Flow recirculation upstream of the propeller at the working point shown by 3D streamlines clipped by a middle plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Contraction of the core flow under the effect of the swirling back-flow . . . . . . . . . 98 Types of flow in an axial turbomachine depending on the throttle position (adapted from Eck [25]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Performance evaluation of the 14F RCP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 CFD calculated static efficiency of the P14 propeller-pump . . . . . . . . . . . . . . . . 100 Iterative adjustment of the propeller twist (pAoA) shown at two exemplary radii of D25: at hub and at an arbitrary radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Chord distribution and Re of the P14 and of the D25 propeller . . . . . . . . . . . . . . 102 Grid study results for one of the new designed propellers . . . . . . . . . . . . . . . . . 102 3D Streamlines of the D25 propellers (0°,10°,20°) at the duty flow-rate . . . . . . . . . . 103

XIII

List of Figures

3.4.20 Inflow profiles of the axial velocity for the investigated D25 designs anlyzed at the duty point (distance between profiles is not to scale) . . . . . . . . . . . . . . . . . . . . . . 3.4.21 Surface of evaluation for the through flow-rate . . . . . . . . . . . . . . . . . . . . . . . 3.4.22 Comparison between the three D25 propellers at the duty flow-rate . . . . . . . . . . . 3.4.23 Projected velocity vectors on a middle plane of the D25 p AO A 20 design . . . . . . . . 3.4.24 Comparison of the airfoils between the D25 and D19 designs . . . . . . . . . . . . . . . 3.4.25 Radial chord and Re-number distribution for P14, D25 and D19 . . . . . . . . . . . . . 3.4.26 3D Streamlines of the D25, D19 and D21 propeller run at the duty point . . . . . . . . 3.4.27 Through-flow, thrust and static pressure compared for D25 D19 and D21 at duty flowrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.28 Pressure flow-rate curves of P14, D19,D21 and D25 (20° twist) . . . . . . . . . . . . . . 3.4.29 Comparison of the through-flow, thrust and ∆P st between 14F RCP and new designed propellers at the duty flow-rate (5 l /mi n) . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.30 Sketch for the momentum theory applied to a propeller in a pipe (adapted from [110]) 3.4.31 Pressure flow-rate measurement results with and without helping device . . . . . . . 3.4.32 Sketch of a propeller slipstream with inlet radius equal to the pipe’s radius . . . . . . 3.4.33 Fast product development showing from left to right: CFD model, CAD model and ready to test prototype (D19) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.34 Validation of the CFD simulation by measurements on the test rig . . . . . . . . . . . . 3.4.35 Computed blood damage index (BDI) for all investigated designs . . . . . . . . . . . . 3.4.36 Average BDI for all investigated designs . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.37 Average exposure time of the investigated pumps . . . . . . . . . . . . . . . . . . . . . . 3.4.38 Stress (σ) volume distribution for all pump cases . . . . . . . . . . . . . . . . . . . . . . 3.4.39 Graphical plot of volumes with values of σ > 150 P a . . . . . . . . . . . . . . . . . . . . 3.4.40 Surface streamlines on the propeller blade . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.41 Blade surface analysis of stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.42 Stresses in the range 50 − 150 P a (medium stresses) . . . . . . . . . . . . . . . . . . . . 3.4.43 Transient flow-rate and pressure used as boundary conditions in CFX (LHS: medical units;RHS: SI units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.44 Transient static pressure measured at the outlet of the domain . . . . . . . . . . . . .

103 104 104 105 105 106 106 107 107 108 108 109 109 110 111 113 113 114 115 115 116 117 117 118 119

A.0.1 Fluid volume with figured stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 C.0.1 LHS: Graupner rMultiSpeed 280, RHS: Placement of the helping device . . . . . . . . 137

XIV

List of Tables

2.1.1 2.1.2 2.5.1 2.5.2 2.5.3 2.6.1 2.6.2

MCL settings for patients with LFVM [75] . . . . . . . . . . . . . . . . . . . . . . . . . . Ideal LVAD propeller duty point parameters . . . . . . . . . . . . . . . . . . . . . . . . . Measured parameters and their range . . . . . . . . . . . . . . . . . . . . . . . . . . . . Components of the test rig shown in figure 2.5.5 . . . . . . . . . . . . . . . . . . . . . . Values used for the benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mock components in analogy to the human circulatory system shown in figure 2.6.1 Average values used to set the mock for ”healthy” condition . . . . . . . . . . . . . . .

. . . . . . .

12 12 38 40 48 51 52

3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.3.1 3.3.2 3.3.3 3.3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5

Summary of the investigated flat plate solution . . . . . . . . . . . . . . . . . . . . . . . Discretization results over a flat plate airfoil at an AO A of 5° . . . . . . . . . . . . . . . Evaluation error of the c l by using the CVL method for airfoil with different cambers Comparison of desired and realized c l for different mean-lines . . . . . . . . . . . . . Comparison of desired and realized c l for mean-lines stand-alone and in cascades . Geometric and performance design parameters of the investigated propeller . . . . . Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design parameters of the investigated propellers . . . . . . . . . . . . . . . . . . . . . . Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Area averaged y+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties of the solid phase (RBC) in CFX, mass flow computed according to [119] . Comparison between the pressure increase in the steady and unsteady simulation .

. 58 . 61 . 63 . 66 . 67 . 76 . 78 . 78 . 84 . 94 . 94 . 96 . 112 . 119

B.0.1 Computation of RBC mass-flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

XV

Nomenclature

Acronyms Symbol Description AD AP Advanced Design of Axial Propellers and Pumps Program AH F

Acute Heart Failure

AH F S Acute Heart Failure Syndrome AO A

Angle of Attack

AP D

Avalanche Photodiode

BDI

Blood Damaging Index

B E M Blade Element Method CFD

Computational Fluid Dynamics

CO

Cardiac Output

C oD

Chord over Diameter, non-dimensional chord distribution

C PU

Central Processing Unit

C RW

Counter Rotating Wall

CS

Cardiogenic Shock

CV L

Cascade Vortex Lattice

DE S

Detached Eddy Simulation

DNS

Direct Numerical Simulation

EKG

Electrocardiogram

FDA

Food and Drugs Administration

F FC

Failing Fontan Circulation

FFT

Fast Fourier Transformation

GU I

Guided User Interface

XVII

Nomenclature

HF

Heart Failure

I AB P Intraaortic Balloon Pump L AP

Left Atrium Pressure

LD A

Laser Doppler Anemometry

LE S

Large Eddy Simulation

LST M Lehrstuhl fur Strömungsmechanik, Universität Erlangen-Nürnberg LV

Left Ventricle

LV AD Left Ventricular Assist Device LV F M Left Ventricular Failure Model M AP Mean Aortic Pressure MC L

Mock Circulatory Loop

N AC A National Advisory Committee for Aeronautics N AS A National Aeronautics and Space Administration N SE

Navier-Stokes Equations

p AO A prescribed angle of attack P AP

Pulmonary Artery Pressure

PV L

Propeller Vortex Lattice

R AN S Reynold Averge Navier Stokes R AP

Right Atrium Pressure

RBC

Red Blood Cells

RC P

Reitan Catheter Pump

S AS

Scale Adaptive Simulation

SST

Shear Stress Transport turbulence model

V AD

Ventricular Assist Device

V LM Vortex Lattice Method

Dimensionless Numbers Symbol Description

Definition

φ

φ=

XVIII

flow coefficient

V˙ N · D3

Nomenclature Y

ψ

head coefficient

ψ=

CP

propeller power coefficient

CP =

Cp

pressure coefficient

u Cp = 1 − V∞

CT

propeller thrust coefficient

CT =

J

propeller advance coefficient

J=

KQ

propeller torque coefficient

KQ =

Q ρn 2 D 5

KT

propeller thrust coefficient

KT =

T ρn 2 D 4

DS

specific diameter

DS =

NS

specific speed

NS =

N 2 · D2 2P 3 ρ A P V∞ µ

¶2

2T 2 ρ A P V∞

V∞ nD

Ψ1/4 Φ1/2 Φ1/2 Ψ3/4

Greek Symbols Symbol Description

Dimensions

Units

α

Angle of Attack

²

drag-to-lift ratio

-

²=

η

efficiency

-

-

λ

cascade stagger angle

-

°

λ

propeller advance ratio

-

λ=

λf

pipe friction factor

-

λf = ζ ·

λL

laser wavelength

L

m

µ

dynamic viscosity

F/A · t

Pa s

ν

kinematic viscosity

F/A · t

Pa s

Ω

rotational speed

rot/t

rev/s

ω

angular velocity

rad/t

rad/s

φ

flow angle on a blade element

-

°

ρ

density

W/V

kg/m3

° Cd Cl

V∞ ΩR d L

XIX

Nomenclature σ

cascade solidity

-

-

τ

shear stress

F/A

Pa

ζ

displacement velocity ratio

-

ζ=

α, β

Heuser and Opitz constants

-

-

Symbol Description

Dimensions

Units

B

number of blades

-

-

I 10 , I 20

thrust radial gradients

-

-

J 10 , J 20

torque radial gradients

-

-

R

tip radius

L

m

r

radial coordinate

L

m

t /l

cascade pitch-to-chord ratio

-

-

wn

total velocity of the propeller slipstream

L/t

m/s

wt

tangential velocity of the propeller slipstream

L/t

m/s

˙ m

mass flow rate

W/t

kg/s

V˙

volumetric flow rate

V/t

m3 /s

∆Hb

plasma free hemoglobin

W/V

mg/L

Hb

hemoglobin

W/V

mg/L

A

area

L2

m2

a

axial interference factor of a propeller

-

-

a0

angular interference factor of a propeller

-

-

C

Heuser and Opitz constant

-

-

c

airfoil chord

-

-

cd

drag coefficient

-

-

cl

lift coefficient

-

-

E

kinetik energy

L2 W/t−2

Nm

e

shear rate

1/t

s−1

f

airfoil camber

-

-

G

Glauert factor

-

-

v0 V∞

Roman Symbols

XX

Nomenclature

l

cascade airfoil chord

N

turning speed

P

pressure

P

Pa

Q

torque

FL

Nm

S

source term for the scalar transport equation

-

-

T

thrust

F

N

t

cascade airfoil pinch

-

-

V

velocity

L/t

m/s

v

velocity

L/t

m/s

v0

displacement velocity

L/t

m/s

x, y, z spatial coordinates in cartesian coordinate system

L

m

Y

FL

J

specific work input (turbomachines)

-

rpm

Superscripts Symbol Description A

test

Subscripts Symbol Description ∞

infinity

i

ideal - used for AOA and lift coefficient

s

related to propeller’s slipstream

st

related to a static quantity

t

turbulent

ti p

tip

t ot

related to a total quantity

XXI

Abstract

This work addresses the development and optimization of propellers in particular of propeller-pumps used in cardiac support (left ventricular assist devices). A novel propeller design method is firstly validated for high-Re marine, multiblade propellers and is adapted afterward for designing small propeller-pumps used as left ventricular assist devices. The initial design framework (ADAP) is fully inverse for the case of marine propellers and is coupled with 3D CFD calculations. In addition, for marine propellers, a Blade Element Method (BEM) is developed for predicting off-design performance. The propeller designer can thus engage in a much faster goal-oriented design parameter search without the use of full 3D-CFD calculations. For the cardiac propeller-pump the design is performed both direct and inverse and has to be always accompanied by CFD simulations. The complexity of the flow around an encased propeller prevents the propeller designer from using BEM in this case. A propeller design framework (ADAP) with different radial momentum loss theories was developed in Matlab r and validated against state of the art vortex-lattice methods. ADAP was programmed to write geometry data to grid generators (e.q. ANSYS TurboGrid r) reducing the time needed from aerodynamic design to CFD simulation. It can also write structured data files which are needed for CAD systems for parametric generation of geometries. In the present work the interface was written for Creo r. Instead of using only predefined NACA camber lines for the radial sections of propellers the framework is improved by implementing a novel method of computing thin airfoil cascades. This method is helpful in the case of designing propellers with more than 4 blades, where blade to blade effects are significant, as for example in the case of propellers used for large container ships. CFD results showed that by using the design code presented in this thesis the thrust of a 6 blades marine propeller was improved by 3.5% and was accompanied by a small propulsive efficiency improvement. Different thickness distributions are implemented in the framework allowing designers to choose the proper one for each application. ADAP was adapted for small diameter propellers-pumps and together with CFD simulations is shown that it can be used for an iterative improvement of a left ventricular assist device. The work also shows that this type of turbomachine working at the duty point required by the human body is off the optimal design. An iterative optimization with different twist angles for the propeller blades was required so that a relationship between blade twist, pressure increase and propeller through-flow was established. Fast propeller-pump designing was possible in ADAP and relevant aspects of the physics flow were analyzed using CFD simulations. Stationary CFD simplifies the complex flow physics and therefore experimental confirmation is required. A modular test-rig was developed for the stationary measurement of the LVAD propellerpump performance. The performance improvement achieved in the CFD was confirmed by measurements on the test-rig. A second test rig simulating the instationary conditions in the human body (MOCK) was developed and used for the validation of time-dependent simulations. The present work has shown that pressure characteristics of propeller-pumps can be improved without increasing blood damage. The presented framework was essential in avoiding the prohibitive computational cost of standard CFD simulations.

XXIII

Zusammenfassung

Diese Arbeit befasst sich mit der Entwicklung und Optimierung von Propellern, insbesondere von Propeller-Pumpen, die als linksventrikuläre Unterstützungspumpen verwendet werden. Ein neuartiges Propellerauslegungsprogramm wurde zunächst für Schiffspropeller validiert. Dieses Auslegungsprogramm wurde danach für die Auslegung kleiner Propellerpumpen, die als linksventrikuläre Unterstützungspumpen verwendet werden, angepasst. Das ursprüngliche inverse Auslegungsprogramm ist mit 3D-CFD-Berechnungen gekoppelt. Darüber hinaus wurde, für die Vorhersage von Off-Design Performance von Schiffspropellern, eine Blade-Element-Methode (BEM) programmiert. Dies ermöglicht dem Propeller Designer eine wesentlich schnellere zielorientierte Designparameterstudie ohne Verwendung von vollen 3D-CFD-Berechnungen. Bei der Herzunterstützungspumpe wurde die Auslegung sowohl direkt als auch invers ausgeführt, wobei sie immer von CFD-Simulationen begleitet wurde. Die Komplexität der Strömung um einen umhüllten Propeller hindert den Propellerausleger in diesem Fall die BEM zu verwenden. Ein Propellerauslegungsprogramm (ADAP) mit unterschiedlichen radialen Impulsverlust-Theorien wurde gegen Stand der Technik Vortex-Lattice-Methoden validiert. ADAP wurde in Matlab programmiert r, um Geometriedaten an Gittergeneratoren (z.B. ANSYS TurboGrid ®) zu schreiben, wodurch die Zeit vom aerodynamischen Design zur CFD-Simulation reduziert wurde. Es kann auch strukturierte Datendateien schreiben, die für CAD-Systeme zur parametrischen Erzeugung von Geometrien benötigt werden. In der vorliegenden Arbeit wurde die Schnittstelle für Creo ® erzeugt. Anstelle der Verwendung von vorgegebenen NACA Profilsehnen wurde das Auslegungsprogramm durch die Implementierung eines neuartigen Verfahrens zur Berechnung dünner Gitterprofilen verbessert (CVL). Dieses Verfahren ist hilfreich bei der Auslegung von Propellern mit mehr als 4 Schaufeln, wobei die Schaufel-zu-Schaufel-Effekte signifikant sind, wie zum Beispiel bei Propellern, die für große Containerschiffe verwendet werden. CFD Ergebnisse zeigten, dass durch die Verwendung von ADAP mit CVL der Schub eines 6 blättriges Schiffspropellers um 3.5% verbessert wurde. Dazu wurde auch der Wirkungsgrad des Propellers leicht angehoben. Durch die Implementierung von verschiedenen Dickenverteilungen in ADAP steht Propellerentwickler immer die richtige Wahl für ihre Anwendung zur Verfügung. ADAP wurde für Propellerpumpen mit kleinem Durchmesser angepasst und zusammen mit CFDSimulation wurde gezeigt, dass es für die Verbesserung einer linksventrikulärer Unterstützungspumpe verwendet werden kann. In dieser Arbeit wurde gezeigt, dass diese Art von Turbomaschine, die am Arbeitspunkt des menschlichen Kreislaufs angepasst ist, nicht optimal als Propellerpumpe ausgelegt werden kann. Dies führte zu einer iterativen Optimierung mit unterschiedlichen Winkeln für die Propellerschaufel, so dass eine Beziehung zwischen Winkel, Druckerhöhung und Propellerdurchfluss hergestellt wurde. Eine schnelle Propellerpumpenauslegung war in ADAP möglich und durch die Verwendung von CFD-Simulationen wurden Aspekte der Strömungsphysik analysiert. Stationäres CFD vereinfacht die komplexe Strömungsphysik, so dass eine experimentelle Validierung erforderlich ist. Für die stationäre Messung der LVAD-Propellerpumpe wurde ein modularer Prüfstand entwickelt. Die im CFD erzielte Verbesserung wurde durch Messungen am Prüfstand bestätigt. Für die Validierung zeitabhängiger Simulationen wurde ein zweiter Prüfstand entwickelt, der die instationären Zustände im menschlichen Körper simuliert (MOCK).

XXV

Nomenclature

Die vorliegende Arbeit zeigt, dass die Druckcharakteristik von umhüllten Propellerpumpen durch das neu entwickelte Auslegungsverfahren verbessert werden kann, ohne die Blutschädigung zu beeinträchtigen.

XXVI

Chapter 1 Introduction

Today’s technologies enable humans longer life expectation and higher life quality. This is possible due to a rapid development of devices and methods which are proactively involved in daily life, either as support or replacement of organs. Such devices are, for example, breathing help devices, circulatory support devices, or artificial arms and legs. Circulatory support devices are used more often because of the dramatically increasing number of patients with cardiac problems. According to Nichols et al. [63] over 4 million deaths were caused in 2011 in Europe due to heart or circulatory problems. From this figure almost a half (47%) is accounted by Cardio Vascular Disease (CVD). Heart Failure (HF) is the cause of about 1 million hospitalizations per year in the USA and Europe [70]. It is anticipated that in the future even more patients will need hospital care due to ageing [70]. In recent years the usage of cardiac support devices has been established among the therapies used in the treatment of the Acute Heart Failure Syndrome (AHFS). Devices are either Ventricular Assist Devices (VADs) or Left Ventricular Assist Devices (LVADs) and can support the circulatory system alone, in parallel, or in series with the human heart. VADs improve the hemodynamics and can also accelerate the restoration of the heart after a HF by decreasing the infarct size [102, 90]. In the cases of pulmonary congestion LVADs decrease the Pulmonary Artery Pressure (PAP) or improve the symptoms of renal deficiency [76]. They are used as a bridge-to-transplant, while the patient awaits a heart transplant, or as a destination therapy for long time support. Although cardiac support devices have been in use for over four decades their design with regard to the biocompatibility, and in particular blood damage could be assessed only in the past 15-20 years. In the context of this thesis biocompatibility is defined as the ability of a device to be in contact with a living system without affecting it in negative way [112]. A high impact on the design of these devices has the usage of Computational Fluid Dynamics (CFD); both for assessing hemodynamic performances and blood damage computation. Questions regarding the methodology of blood damage prediction as well as the principles used in the design of devices are concerning researchers all over the world. Due to the fact that there are several types of pumps used in the cardiac support, one has to expect that they will behave differently in similar conditions. HF is a clinical syndrome initiated by abnormal function of the heart [79] and which can be explained as the inability of the heart to provide the pump work required to maintain the perfusion of the organs [74]. AHFS’s are one of the most common causes of hospitalization for patients older than 65 years in the USA [17]. According to the same source, the number of hospitalizations will continue to grow in the coming years as a result of an aging population and due to the improved survival after myocardial infarction. The demand for a VAD that can be used for short term support as well as a long-term destination therapy device has increased as well. As the number of patients with AHFS is expected to increase even more in the next years, an increase in the demand of reliable LVAD is also expected. Cardiogenic shock (CS) is defined as an acute heart failure (AHF) caused by a heart function disorder and has as result the hypoperfusion and hypoxia of organs [58][55]. Recent studies have shown that in the case of an CS the proportion of perfused vessels in micro vascular tissues is decreased due to their inability to dilate as response to hypoxia [46]. CS has an incidence of 1% from all cases of AHFS [17] and according to Michels and Schneider T. [58] between 5 and 8% among the patients with

1

Chapter 1 Introduction

myocardial infarction. Killip classifies CS as the most critical stage of a myocardial infarction (Stage IV) [58]. The target of the therapy for patients in CS is the fast improvement of the cardiac pump function [17]. This is required also in order to keep the perfusion and oxygenation of the organs. The treatment of CS can be done either by medication or by using a VAD [58]. In case patients are not responding to the medication the use of an Intraaortic Balloon Pump (IABP) is recommended [58].

1.1 Short overview of LVAD used in the treatment of cardiogenic shock Intra-aortic Balloon Pump The working principle of the Intra-aortic Balloon Pump (IABP) is based on counter-pulsation which is achieved by an external pumping chamber (figure 1.1.1). During the diastole the balloon inflates creating a counter pressure and then deflates during the systole. The inflating-deflating of the balloon is controlled by an electrocardiogram (EKG) or blood-pressure signal. The balloon pump was first developed in the early 1960s and is enjoying a wide acceptance today. Because of its counter-pulsating principle this pump can be used only when the heart is still active.

Diastole

Systole

Figure 1.1.1: The Intra-aortic balloon pump (from [115])

Hemopump Another device developed for use in the CS is the Hemopump® (figure 1.1.2). It was developed specifically to be used for CS, during minimally invasive coronary bypass surgery, and for pathologies in which the heart must be relieved of approximately 80% of its workload [93]. The main difference compared to the IABP is that Hemopump® is an axial continuous flow pumping device whose pumping principle is based on the Archimedes’s screw design. The Hemopump® could be placed inside the ventricle through different blood vessels and achieved a higher Left Ventricle (LV) unloading than the IABP [90]. It has been the first axial blood pump ever used [97]. The Hemopump® is no longer available for clinical use.

Impella A similar screw design is adopted by Impella (2.5 and 5.0)1 ; a device currently in clinical use. Like Hemopump, it is an in-ventricle implantable LVAD of very small dimensions 3 mm or 9 F , which can be inserted in the aorta through catheterization (figure 1.1.3). The pump has two blades of 0.3 mm 1 2.5 and 5.0 stand for the maximum cardiac output (http://www.abiomed.com/products/)

2

1.1 Short overview of LVAD used in the treatment of cardiogenic shock

Figure 1.1.2: Hemopump®[97]

thickness, which rotate at a speed of 33000 r pm and has a tip gap of only 0.1 mm [93]. The small version (Impella 2.5) is implanted through the femoral artery while Impella 5.0 needs femoral artery surgery. Impella is still associated with high hemolysis which demands an anti-coagulation therapy [4].

Figure 1.1.3: Impella 2.5 ® von Thoratec® and its placement [102]

Reitan Catheter Pump (RCP) An alternative to the IAPB has been presented in 1999, the Reitan Catheter Pump (RCP), which is an axial propeller-pump (figure 1.1.4)[77]. From the turbomachinery classification this device can be defined as an encased propeller. It has been designed as a short term continuous flow rotating systemic circulatory support device. The target patients for this device are myocardial infarction patients in AHF or in CS, and patients having coronary angioplasty. Conceptually, it is an axial two bladed propeller-pump spinning at speeds ranging from 1,000 to 14,000 rpm. The blades have a diameter of 15 mm and the diameter with the protective cage is 21 mm (figure 1.1.4).

Figure 1.1.4: 14F Reitan catheter pump (figure courtesy of Cardiobridge Gmbh/Hechingen)

3

Chapter 1 Introduction

The pump head is foldable like an umbrella resulting in a diameter in folded (closed) position of 4.67 [mm] (14) F . This eases the insertion of the pump which is done percutaneous by using an inducer in the femoral artery. After insertion it is slowly pushed up until it reaches the upper side of the descending aorta and then unfolded (figure 1.1.5).

Figure 1.1.5: Physiological position of the 14 F RCP in the upper aorta (figure courtesy of Cardiobridge Gmbh/Hechingen) Figure 1.1.5 shows the open RCP positioned in the upper aorta just after the aortic arch. In this position the pressure gradient over the pump increases the irrigation of vital organs fed from the main aorta (e.g. kidneys and liver). The rotation of the blades is assured by a flexible shaft inside the catheter which is connected to an external driving unit. Several animal and human clinical studies [74, 77, 91] have proven the benefits of the RCP in recent years, but the device is not yet commercially available2 . Similar (axial) propeller-pump concepts have been presented for the treatment of Failing Fontan Circulation (FFC) [104, 103]. They are running at much lower speeds, and there is no evidence that these devices are designed to increase blood pressure at flow-rates between 4 to 5 l/min, which are the target flow-rates in the CS. The benefits of a folding propeller-pump can be briefly summarized: • easy insertion in the femoral arteries, similar to the use of IABP • easy deployment • due to a very large tip gap a low hemolysis is expected which was observed in vivo by Smith et al. [91] • reduced risk of thrombosis by a reduced risk of the activation of platelets by minimal foreign surface exposure (shroud is the blood vessel Throckmorton et al. [104]) • swirling flow at the exit of the propeller inducing transverse velocities on the blood vessels and reducing the risk of stagnation. The hemodynamic design of such a device influences directly not only the pumping performance such as head or efficiency but also the biocompatibility (hemolysis in this case). Common to many of the rotating pumps used in the cardiac support is the way they were designed: directly, mostly by trial, and error. This method, although it is straight, demands a higher effort in terms of time since there are many iterations needed until the aimed performance is achieved. An alternative to this is the inverse design method, which allows the engineer the lay-out of a device only by knowing the duty points. However, this method requires the knowledge of the device’s physics and deep fluid dynamic understanding. 2 as of December 2016

4

1.2 Design and analysis methods for VADs

1.2 Design and analysis methods for VADs Designing a turbomachine can be a complex task depending on the duty-point, fluid medium, or other conditions imposed. Designing a VAD is challenging because of its dimensions, because of the fluid medium and because of the biocompatibility which has to be guaranteed. These challenges are constrained by material strength and material compatibility with biological tissues. Throckmorton treats in depth the problem of propeller-pump design [104] and suggests the use of empirical equations and CFD simulations for geometry optimization. Clearly this is a good way to design pumps and it is also the method followed by most blood pump designers. In literature concerning turbomachinery design, it is usually known as the direct design method and basically means, that a pump geometry is created using empirical formulas and then adjusted by trials in order to achieve the desired performances. It is a very costly and time intensive process. In contrast, inverse design is based on a set of simplified fluid flow equations linked to the geometry (airfoils, camber-lines, vortex distribution) and which deliver a geometry capable of fulfilling the design requirements. The geometry is also verified by CFD means. Both design strategies are available in commercial codes. Several open source codes are available for propeller design: OpenProp [26], Xrotor/Qprop [23] or Qblade [53]. A detailed analysis of existing design methods for propellers is given in section §2.4. Computational Fluid Dynamics (CFD) is a tool used in today’s engineering practice for the development of many cardiac support devices. CFD is mainly used as a replacement to experimental measurements of pressure-flow curves and it offers, depending on the complexity of simulation, a deeper look in the physics of the flow. This contributes to the understanding of complex phenomena taking place in devices and thus to their enhancement. Hemolysis, the damage of red blood cells or erythrocytes (RBC), can be evaluated by computing the Blood Damaging Index (BDI) from the results of CFD simulations. This is performed with the formulation of scalar stresses firstly given and validated by Bludszuweit [13],[14]. No deeper details about the numerical schemes of CFD codes are given here since this does not make the object of the present work, but descriptions of methods, algorithms, and their implementation are given in Blazek [12], Hirsch [38] or Ferziger and Peric [30]. Even with today’s advances in computational simulation one can not replace the experimental validation. For medical devices the experimental validation has to be carried out directly on animals and lately on humans, in vivo3 . The most usual way to asses performances of VADs is to measure the pressure flow-rate curve on a test rig. The construction of a test rig capable of measuring precisely the flow-rate and pressure increase is thus very important. The measurement of a VAD is more complex in conditions similar to in vivo conditions: in a Mock Circulatory Loop (MCL) or simply mock4 . This test rig is basically a dynamic replica of the human circulatory system and provides ideal conditions for performance or endurance tests of VADs.

1.3 Outline and objectives of the dissertation The second chapter of this dissertation reviews the useful literature needed to accomplish this work. It starts with an introduction in the physiologic foundations of the human circulatory system which is complemented by a description of blood and blood damage prediction using CFD methodology. HF and the CS are condensed with the help of numbers and the Cordier diagram in duty points for the future propeller-pump. This is followed by an introduction in the fluid mechanics and a short description of turbulence modeling methodology used in modern CFD codes. Airfoils play an important role in the design of propellers, therefore an introduction is given afterward. This is followed by a section covering all aspects of modern propeller design methods. Validation plays an important 3 a study in vivo refers to study in a living organism - www.wikipedia.org, accessed on the 27.12.2016 4 mock is synonym of imitation or simulation

5

Chapter 1 Introduction

role in the design of turbomachinery and this is accomplished by using test rigs. The design and construction of test rigs for VADs both for measuring in steady state condition and pulsating flow (MCL) is shown at the end of the second chapter. Following the second chapter a method is developed for assessing the performance of airfoils in cascades by using potential methods. This is implemented in a propeller design code using a new semiempirical approach for computing the blade losses by using the Goldstein method. The validation of the cascade code for designing multiblade open-water propellers is shown subsequently. It is shown by CFD simulations that the thrust of propellers can be improved by 3.6% at the propeller design point without penalties in the efficiency by using the new airfoil cascade analysis method. Parameter studies are performed in this chapter for choosing the correct propeller design variables. The validation of the propeller design code delivers the foundation for the design of propeller pumps used as VADs in the next section. Here is shown, however, that the actual challenge is not only the design itself but understanding the flow mechanisms produced by a propeller in a pipe. The overall goal is the performance improvement in form of pressure rise of the existing P 14F RCP without affecting its biocompatibility. The main dimensions (D t i p , D hub ) and other general characteristics (speed and design flow-rate) of the propeller are fixed. The performance of the reference propeller (14F RCP) is described and analyzed in subsection 2.1.5 and subsequently in subsection 3.4.1 and it is used to calibrate the CFD tools with the help of a measurement data provided by the test stands. As an answer to the direct design approach used in the typical LVAD design, this work proposes a modified propeller inverse design method. Due to the very low Re-number flows in VADs the method is first validated on marine propellers. Briefly formulated, the specific objectives of the research in this dissertation are : • increase the pressure rise of the propeller-pump for the same flow-rate • decrease the shear stresses generated by the propeller • decrease the resident time spent by the RBC while flowing around the propeller Most promising designs are built as prototypes and validated on the test rig. Their blood damaging index (BDI) is evaluated afterwards by using state of the art methods exposed in the second chapter. Finally, one of the designs, together with the baseline 14 RCP, is evaluated using transient CFD simulation using boundary conditions derived from the MCL setup. Finally the outcomes of this thesis are presented, both on the design methodology side as well as on the required VAD development itself. Benefits and drawbacks of the propeller design methodology presented in the thesis are reviewed and discussed. The improvements achieved for designing the propeller-pumps are discussed together with results from the literature and an outlook for future work is presented.

6

Chapter 2 Selected aspects in relevant areas for the design of VADs

This chapter summarizes fundamental knowledge needed for the design, simulation and experimental validation of VADs. It contains a literature review about the physiology of the circulatory system and of the heart, figures regarding the desired and real duty point of propeller-pumps, fundamental fluid mechanics and airfoils, propeller design and the experimental test stands used for validation in this thesis. The reader can understand the actual challenges in the development and design of VADs.

2.1 Design consideration for VADs To understand the clinical meaning of the CS and HF it is necessary to know where and how they take place. In this section the anatomy and physiology of the circulatory system and of the human heart is briefly described. The most important factors contributing to blood damage are presented together with computational prediction methods. The medical facts of the CS are introduced and the duty points of a VAD are computed and then analyzed in the Cordier diagram.

2.1.1 Human circulatory system One of the essential components of the human body is the circulatory system. The fluid in the system is blood which transports oxygen and the nutrition to body cells and CO 2 to the lungs in the reversed direction. In the direction to the cells the circulatory system is formed by arteries and capillaries while on the reverse side the circulatory system is formed out of veins as depicted in figure 2.1.1. The circulatory system is composed of two subsystems: the pulmonary circulation system and the systemic circulation system. The center of the circulatory system is the heart which pumps the blood with an average of 5 [l /mi n] 1 through the arteries and veins of the body. To accomplish this effort the heart needs 1W power [67]. The pulmonary circulatory system is powered by the right side of the heart being placed between the right ventricle and left atrium as depicted in figure 2.1.1. The heart is a muscular organ which pumps the blood in the circulatory system by a cyclical contraction (systole) and dilatation (diastole). Figure 2.1.1 shows that the heart has two main parts: right atrium and ventricle on one side and left atrium and ventricle on the other side. Pumping is realized synchronously by right and left ventricles during the systole. Atria do not have a pumping function. 1 average for healthy adult

7

Chapter 2 Selected aspects in relevant areas for the design of VADs

Figure 2.1.1: Human circulatory system [1]

2.1.2 Blood composition and its physical properties Blood is the fluid in the circulatory system with an average volume of 5, 2 l and represents 8% ± 1% from the total body weight [85]. It is composed of a fluid part called blood plasma, which is mixed with suspended solids called blood cells or hematocytes. The three major blood cell types in the blood plasma are [85]: • red blood cells (RBC- erythrocytes - totalizing about 95% of all cells), • white blood cells (leukocytes - representing 0.15%), • platelets (trombocytes - representing less than 5%) . Blood plasma consists of water (90%) and proteins (7%) and has a viscosity 1.5 higher than that of water. The density is above that of water, 1.035 kg /m 3 . Erythrocytes have the role of transporting blood gases from and to the cells in the body and have the shape of biconcave discs with a diameter of 7.5 µm [119]. The volumetric fraction of erythrocytes in blood is called hematocrit and has values usually around 45%. Trombocytes are involved in the blood clotting process while leukocytes have the primary role of protecting the body from external organisms. Fluids shear at a strain rate inversely proportional to the coefficient of viscosity µ [118]. The strain rate can be related to the shear rate (e = ∂u/∂y) of the flow [118], so the shear stress for a simplified case of one-dimensional steady flow and an isotropic and homogeneous fluid can be written as:

τ=µ

∂u ∂y

(2.1.1)

For a three-dimensional case the relation is given in appendix A. If the relation in equation (2.1.1) is linear one can speak about a Newtonian fluid otherwise the fluid is non-Newtonian. From the rheological point of view the blood plasma can be considered a Newtonian fluid, while the blood with suspended particles may be considered both Newtonian and non- Newtonian. This behavior

8

2.1 Design consideration for VADs

t

Plastic

m Bingham Pseudo-plastic

RBC

103

10

2

Dilatant 101

Newtonian 10

e

0 -1

10-2 10 100 101 102 103

(a) Shear stresses of different fluids (adapted from [24])

e

(b) Blood viscosity as function of shear rate (adapted from [67])

Figure 2.1.2: Rheological properties of blood

will be explained in this section since it is very important for the blood flow modeling. In figure 2.1.2a are shown various cases of non-Newtonian fluids compared to the Newtonian case. Blood viscosity is inversely proportional to the shear rate as shown in figure 2.1.2b. This is caused due to the orientation of RBC under the effect of shear stresses: when RBC are subjected to high stress in motion, they align along flow direction axis, reducing the resistance in the fluid and thus the viscosity [29]; at small shear rates (no or low flow) RBC’s group together in so called roleaux [29]. Both cases are illustrated simplified in figure 2.1.2b. Patients with HF might have different levels of hematocrit than usually seen, between 33% and 36% [111] so it is important to know how the rheological properties are changing according to this. The behavior is shown in figure 2.1.3. Normal hematocrit levels for healthy humans are around 45% [29]. It is important to mention that blood viscosity is influenced also by temperature, but its influence will not be discussed in this thesis since temperature will be considered constant for all investigated cases.

Viscosity [cPoise]

1000 100

H=90%

10

H=45%

1

H=0%

0.1 10-2

10

-1

10

0

101

10

2

-1

e [s ] Figure 2.1.3: Viscosity vs shear rate for different hematocrit levels (adapted from [29])

9

Chapter 2 Selected aspects in relevant areas for the design of VADs Viscosity decreases with decreasing hematocrit level and above a shear rate of 100 [s −1 ] is constant (figure 2.1.3). These results are also used in recent CFD studies upon VADs where the blood was assumed incompressible with constant viscosity [32]. Hence, the blood will be modeled as a Newtonian fluid in this thesis.

2.1.3 Considerations on blood damage for VADs The action of external factors can lead to the deformation or damage of blood cells. Hemolysis and and thrombosis represent the most important kinds of blood damage. Other types of damage are: platelet activation, emboli, reduced functionality of the white blood cells and destruction of the von Willebrand factor [32]. The damage of RBC under the effect of an external force is the result of traumatic fluid stresses acting with a specific amplitude and a specific frequency for a certain amount of time (the ”triple” action, figure 2.1.4). Early investigations proved the relationship between stress, exposure time and hemolysis. Hemolysis reduces the RBC concentration in blood causing a decrease of oxygen transport to the cells. Because of the cell destruction the hemoglobin contained by the RBC is transferred to the plasma. The measurement of hemoglobin concentration in blood quantifies the hemolysis.

Exposure Time

Amplitude

Frequency

Figure 2.1.4: Shear stress factors contributing to the blood damage CFD is an efficient tool for investigating blood hemolysis since it can evaluate stress levels and their exposure times. State of the art models will be presentd and they are used extensively in section §3.4 for the evaluation of the VAD designs proposed in this thesis. The combination of effects was first investigated by Bludszuweit [13], who was also the first to define the comparative stress level in a fluid. The latter are the equivalent of the von Mises criterion used for mechanical stresses. For solids, the threshold level of stresses is given by the yield stress of each specific material. The scalar shear stress (σ) is defined ([13]-appendix A) : r σ=

¢2 X 1 X¡ τi i − τ j j + τ2i j 6

(2.1.2)

Initially a minimal stress threshold, which could cause direct cell damage, has been found experimentally: 150 P a [50]. However, as previously stated, stresses alone can not indicate the hemolysis. According to Taskin et al. [98] there are two models for predicting the hemolysis: strain-based models and power-law models. Power-law models differentiate between two fluid analysis approaches: Eulerian and Lagrangian. The Lagrangian approach is very complex and is based on the evaluation of the stress history of particles which are injected at the inlet of the flow domain. This approach enables the evaluation of hemolysis by all factors: amplitude, time and frequency of stresses. The outcome of

10

2.1 Design consideration for VADs

the approach is the blood damage index (BDI) which is the percentage of damaged blood cells. It is based on the evaluation of the scalar shear stresses experienced by a particle during its traveling time in the fluid domain. This approach is empirical and as a consequence has been best correlated for specific devices. The correlation is performed with the help of exponential coefficients (α and β see equation (2.1.3) ) which are adjusted with the help of regression from experimental data. BDI is then evaluated according to following expression [111], [94]:

B D I (%) =

∆H b · 100 = C · ∆T α · σβ Hb

(2.1.3)

where ∆H b represents the plasma free hemoglobin, and Hb the hemoglobin - both are determined experimentally; C , α, β are the model constants (Heuser and Opitz constants [98]) while the exposure time (∆T ) and σ of each particle are obtained from the simulation. The Lagrangian model was used in the development process of several blood pumps ([111, 105]) and has gained a wide recognition in literature. More precise in the correlation with the experimental data, the model is used for the quantitative comparison of the BDI of the investigated pumps in this thesis. In addition, the σ levels in the fluid volume are analyzed and compared to critical values available in the literature (Eulerian analysis) as for example in [31]. This method enables the VAD designer the chance to analyze visually the stresses produced by a particular pump design. Of course in this way the causes of the possible to high stresses can be evaluated directly from the flow field. In addition to the σ volume analysis Taskin et al. [98] and Fraser et al. [32] proposed more recently an Eulerian approach of calculating the potential blood damage of VADs by using a scalar transport equation: ¡ ¢ d ∆H b 0 dt

¡ ¢ + v · ρ · ∇ ∆H b 0 = S

(2.1.4)

¡ ¢1/α where S is the source term and is defined by S = ρ H b · C · σβ . This model also needs an empirical validation and is therefore also very model-dependent. Taskin et al. [98] have recently published a benchmark between all up-to-date hemolysis models by using available constant and regression coefficients. It was concluded that the Eulerian model hemolysis results do not agree well with experimental results, but because of its well correlated coefficients is very good for relative comparisons. On the other side, the Lagrangian models correlated well with the experimental hemolysis results but the models are highly dependent on the constants.

2.1.4 Design requirements (duty point of a LVAD) Section 1.1 provided the definition of the CS. In order to define a duty point for a blood pump one needs to analyze the relationship between the flow parameters between a healthy and an ill patient. This will lead to figures which define the duty point of the turbomachine. CS can be quantified by a systolic arterial pressure below 90 mmH g 2 or a Mean Aortic Pressure (MAP) 30 mmH g lower than the basal one [39] (in [58] the definition is given as below 70 mmH g ). Left ventricular failure is more often and, in the case the right ventricle functions normally, it leads to a pulmonary oedema (or backward congestion) with high pressure in the pulmonary circulation system according to [74] and [17]. This is the background of a study upon a left ventricular failure model (LVFM) performed by Reitan et al. [78] where the Left Atrium Pressure (LAP) was increased from values of 5−10mmH g to 25mmH g in order to simulate pulmonary oedema. In this model the outcome of a VAD was assessed by the decrease of LAP (decongestion). 2 1 [mm Hg]= 1 [Torr]=133.2 [Pa] - pressure unit intensively used in medicine

11

Chapter 2 Selected aspects in relevant areas for the design of VADs

Diastole

140

18665

120

15999

100

13332

80

10666

60

7999

40

5333 Pout-healthy condition (MOCK)

20

2666

Pout-severe HF - CS (MOCK)

0 0.0

0.3

Time [s]

Poutaortic [Pa]

Pout aortic [mmHg]

Systole

0 0.9

0.6

Figure 2.1.5: Aortic pressure (AoP) distributions for healthy and severe CS - cases

The values determined for LFVM can be set in a MCL in order to simulate the effect of the VAD in vitro. Reitan developed a set of parameters describing the hemodynamics of a patient with LFVM based on measurements performs on 10 patients [75], which are depicted in table 2.1.1. Based on the settings for the normal human heart, a set of parameters designed to reproduce the global dynamics in CS or AHFS have been validated on the MCL. With the values provided by Reitan [75] shown in table 2.1.1 a theoretical curve of the aortic pressure for patients in CS can be determined. This curve is measured on the MCL and the results are plotted against the one of measured healthy heart (in section 2.5.4-figure 2.6.3b) in figure 2.1.5. Table 2.1.1: MCL settings for patients with LFVM [75] CO [l /mi n]

AoP [mmH g ]

MAP [mmH g ]

LAP [mmH g ]

RAP [mmH g ]

Heart rate [mi n −1 ]

4

70/30

50

15

5

70

2.1.5 Head characteristics The encased propeller has to be adapted to the adult circulatory system working in series with the human heart at flow-rates between 2 and 10 l/min and increasing pressure with 10-20mmH g . These are values used in the treatment of cardiogenic shock caused by severe left ventricular failure. Ideally, the propeller LVAD should increase the CO from 4 l /mi n (table 2.1.1) to the normal one (5 l /mi n) and the AoP pressure from 50mmH g to 90mmH g (which is the minimum limit for AHF). The design input data for the propeller VAD are given in table 2.1.2. Table 2.1.2: Ideal LVAD propeller duty point parameters Parameter design flow-rate pressure rise max propeller speed max propeller diameter density

12

Value V˙ ∆P N D ρ

5 l /mi n >40 mmH g ≈ 5328 P a 13000 r pm 15 mm 1035 kg /m 3

2.2 Governing equations for fluid dynamics and aerodynamics

The design of a turbomachine is initiated using the Cordier diagram which links the specific speed (NS ) to the specific diameter (D S ) of a turbomachine. They link the concept of machine type (axial, mixed-flow or radial) to a specific pair of specific speed NS and specific diameter D S .

Figure 2.1.6: Cordier diagram following Lewis [52]showing the ideal and existing design points set for a LVAD

NS =

Φ1/2 Ψ3/4

and

DS =

Ψ1/4 Φ1/2

(2.1.5)

where Φ and Ψ are the flow and head coefficients given by:

Φ=

V˙ N · D3

and

Ψ=

Y N 2 · D2

(2.1.6)

and Y = ∆P /ρ. The pair of Φ, Ψ define the duty point of the turbomachine. With the data presented in table 2.1.2 one can plot the duty point in the Cordier diagram, here in a version adapted from Lewis [52]. In figure 2.1.6 the red point shows the pair of NS and D S for an optimum LVAD as computed with the data from table 2.1.2. The blue point represents the actual measured duty point of the existing 14F RCP. None of the points belongs to axial type but to centrifugal respectively to mixed flow pumps. The difference between the two duty points is a result of the pressure rise difference: the 14F RCP has1900 P a ≈ 14 mmH g while the ideal pump has 5328 P a ≈ 40 mmH g at the same flow rate: 5l /mi n. Since the RCP is an axial propeller-pump but operates as a mixed flow pump it will not operate at its maximum efficiency. The pump will operate at the duty point at off-design condition. These matter will be addressed in detail in the results chapter, in subsection 3.4.

2.2 Governing equations for fluid dynamics and aerodynamics In this thesis propellers will be designed by using simplified fluid dynamics equations. They are virtually tested then in different mediums at high and low Re numbers in different fluids by CFD means. Testing of the propeller pumps occurs in both steady and unsteady flow conditions on different test stands designed to replicate in-vito conditions. In this chapter the fluid mechanics methods employed in the design and simulation of the propellers will be discussed in detail. The versatility of the

13

Chapter 2 Selected aspects in relevant areas for the design of VADs

physiological blood flows investigated in this thesis needs a large variety of CFD simulations: steady, unsteady, one and two-phase. All of them have in common turbulence modeling which is explained briefly. On the other side the flow around turbomachinery blades is treated stationary for the duty points. Usually the design of turbomachinery blading is performed for high Re-Numbers. Governing equations will be simplified to inviscid two-dimensional potential flows which allow the design of air-and hydrofoils.

2.2.1 Governing equations for fluid dynamics Fluid flow is described by the equations of mass, momentum and energy conservation equations [24]. In order to solve the different types of flow, the governing equations of fluid dynamics will be brought in an useful manner. First, the equations of mass and momentum conservation will be arranged in such a way that they can be solved numerically by using turbulence models. A fluid flowing obeys the mass conservation: ∂ρ ∂(ρUi ) =0 + ∂t ∂x i

(2.2.1)

where ρ is the fluid density t is the time and Ui are the velocity components while x i denotes the spatial components (i = 1, 2, 3). For incompressible fluid (ρ = const ant ) equation (2.2.1) simplifies to: ∂Ui =0 ∂x i

(2.2.2)

∂u ∂v ∂w + + =0 ∂x ∂y ∂z

(2.2.3)

which can be written in component form as:

Fluid motion is described by the generalized momentum equation, which is derived for a continuous fluid using the Newton’s second law. For Newtonian fluids the momentum equation simplifies to the Navier-Stokes equations (NSE). The general form of the momentum equation written in index form reads [24]: ∂u i ∂u i 1 ∂P ∂τi k + uk =− + + ρg i ∂t ∂x k ρ ∂x i ∂x k

(2.2.4)

and for a Newtonian fluid the viscous stress differential term can be written: ∂τi k ∂2 u i =υ ∂x k ∂x k ∂x k

(2.2.5)

In the case of a conservative field, the gravitational term can be dropped so equation (2.2.4) using equation (2.2.5) becomes: ∂u i ∂u i 1 ∂P ∂2 u i + uk =− +υ ∂t ∂x k ρ ∂x i ∂x k ∂x k

(2.2.6)

which are the Navier-Stokes equations (NSE) written in index form. To find P and u i the above system of partial differential equations (PDE) can be solved by using specific boundary conditions and initial conditions. Further details can be found in textbooks like [24],[12] and [30].

14

2.2 Governing equations for fluid dynamics and aerodynamics

In engineering practice flows are almost always turbulent and the transition from a laminar to a turbulent state (i.e transition over an airfoil) is very important and is one of the most researched topics in fluid mechanics. Laminar and turbulent flow states are usually defined by the Re (Reynolds) number, named after the British researcher Osborne Reynolds [24]. The Re number defines the ratio between acceleration terms and molecular impulse transport:

Re =

u ·L ν

(2.2.7)

where u is the velocity, L is a specific length and ν is the kinematic viscosity of the medium. To understand the unsteady nature of fluid flow this has to be interpreted in a statistical manner by analyzing the fluctuation of certain quantities around an averaged value. The Reynolds decomposition will be applied to the NSE [24, 40]. Any fluctuating quantity (G) can be decomposed in two main components[40]: G =G +g

(2.2.8)

where: • G is the average part of the quantity (see figure 2.2.1) • g is the fluctuating part of the quantity (seefigure 2.2.1) where the average si defined by:

1 G x, y, z = lim T →∞ T ¡

¢

ZT

¡ ¢ G x, y, z d t

(2.2.9)

0

G g

G G=G+g

t Figure 2.2.1: Local time-average of a fluctuating quantity G Averaging can be applied to the velocity and pressure components leading to: ¡ ¢ ¡ ¢ ¡ ¢ V x, y, z, t = V x, y, z + v x, y, z, t

(2.2.10a)

¡ ¢ ¡ ¢ ¡ ¢ P x, y, z, t = P x, y, z + p x, y, z, t

(2.2.10b)

Using the averaged velocities and pressures equation (2.2.6) can be now written:

15

Chapter 2 Selected aspects in relevant areas for the design of VADs

³ ³ ³ ´ ´ ´ 2 ´ ³ ´ ³ ∂ ∂ ∂ U + u P + p U + u i i i i ∂ 1 U i + ui + U k + uk +υ =− ∂t ∂x k ρ ∂x i ∂x k ∂x k

(2.2.11)

Leading to the Reynolds Averaged Navier-Stokes (RANS) equations: Ã ! ∂ρU i ∂ ∂U i ∂P ∂U i + + ρU k =− ρυ − ρUi Uk ∂t ∂x k ∂x i ∂x k ∂x k

(2.2.12)

The term ρUi Uk is called the Reynolds-Stress-Tensor and represents the closure problem of turbulence models. How this term is handled by different turbulence models affects the evaluation of the other terms in the equation, and hence the computed flow-field.

2.2.2 RANS turbulence modeling CFD programs solve the NSE numerically, in particular the RANS form shown previously in equation (2.2.12). For solving the integro-differential form of the fluid flow equations several methods are commonly used: finite differences, finite element and finite volume methods. Today’s CFD codes prefer the finite volume method which directly utilizes the conservation laws [12] which is the integral formulation of the Navier-Stokes equations. This distinguishes the finite volume method significantly from the finite difference method, since the latter discretizes the differential form of the conservation laws. The concept of RANS and Reynold stresses was introduced previously (equation (2.2.12)). In RANS the closure of the transport equations can be achieved either by solving the components of the Reynolds-Stress-Tensor (by so called Reynolds Stress Models) or by modeling the Reynolds-StressTensor using an eddy viscosity, µt . The two-equation models of turbulence base on the Boussinesq assumption, who proposed that the Reynolds-Stresses should be modeled in the same way as normal and shear stresses [66]. With the Boussinesq assumption the Reynolds stresses can be written: Ã ρUi Uk = µt

∂Ui ∂Uk + ∂x k ∂x i

! (2.2.13)

Apart from the RANS turbulence models, it is today’s practice to include Large Eddy Simulation (LES), Detached Eddy Simulation (DES) or scale adaptive simulation (SAS). They offer a much deeper look in the physics of the fluid problems (see figure 2.2.2) by solving a broad band of time and length scales of the turbulence. The counterpart is that the needed computational effort (time and amount of CPU’s) is much higher than the one needed for a RANS simulations and for many practical applications they are not feasible. However, these methods are still ”modeling” the flow even if only at subgrid scales. In this list should be included also the direct numerical simulation (DNS). This kind of simulation does not model any turbulence scale but solves it accurately in time and space. However, DNS simulations need a very fine computational grid and a very large amount of time. Referring to RANS modeling the less computing intensive methods are the ones using the model of eddy viscosity. But it is easy to note while looking at figure 2.2.2 that RANS is modeling near-wall flows and solves only the bulk flow. Eddy viscosity models include: • zero-equation models (or algebraic turbulence models) i.e.: Prandtl mixing-length model, BaldwinLomax model, Cebeci-Smith model • one-equation models i.e.: Spalart-Allmaras • two-equation models like: k − ², k − ω, Shear Stress Transport turbulence model SST

16

2.2 Governing equations for fluid dynamics and aerodynamics

Large scales

102

Energy containing integral scales

Inertial subrange

Viscous subrange

101 -5/3

k

E

100 10-1 10-2 10-3

10-2 Computed by RANS

10-1 k

100

Modeled by RANS Solved by LES

Computed by LES

Solved by DNS

Figure 2.2.2: Energy spectrum of turbulence as function of the wave number k with the application range of CFD turbulence models (adapted from Hirsch [38, pp.88])

Bardina et al. [7] have investigated the prediction of RANS turbulence models [7] and concluded that the SST model [57] has the best overall prediction results for complex flows. Its unique capability to predict flow separation in steady state simulations was found remarkable by the investigators. This is achieved by switching between two turbulence models in the same model: k − ω at boundaries and k −² in the bulk flow. By combining these two models, the deficits of both are overcome: the excessive turbulence production at the wall of the k − ² model (as described by Menter [56]) and the sensitivity of the k − ω model in free flows. The model has gained a lot of attention since its first presentation by Menter [57] because it can solve very well flows with adverse pressure gradients (such as airfoils at higher angles of attack), which are found in all aerodynamic and hydrodynamic applications. Hirsch [38] showed that the SST turbulence model has the best predicting capability for a diffuser-case when compared to other turbulence models, while in [9] the k − ² model for simulating the performance characteristics of open-water marine propellers has been used. Later CFD results shown that the efficiency was under-predicted when compared to the experiments. The fact that SST offers reliable results needing reasonable computational time, when compared to other models, lead to the decision to use the SST turbulence model for the CFD simulations in this thesis. Adaptive wall functions are used in this model which verify at every vertex near the walls, if they are yet below or above the boundary layer limit; in the case the grid is fine enough (at least 10 cells grid cells in the layer (y+